Pulsed Evolution Shaped Modern Vertebrate Body Sizes

Pulsed evolution shaped modern vertebrate body sizes

Michael J. Landisa and Joshua G. Schraiberb,c,1

aDepartment of Ecology and Evolutionary Biology, Yale University, New Haven, CT 06520; bDepartment of Biology, Temple University, Philadelphia, PA 19122; and cInstitute for Genomics and Evolutionary Medicine, Temple University, Philadelphia, PA 19122

Edited by Neil H. Shubin, The University of Chicago, Chicago, IL, and approved October 6, 2017 (received for review June 18, 2017) The relative importance of different modes of evolution in shap- ties of these methods, nor is much known about the prevalence of ing phenotypic diversity remains a hotly debated question. Fos- pulsed change throughout some of Earth’s most intensely stud- sil data suggest that stasis may be a common mode of evolution, ied clades. while modern data suggest some lineages experience very fast Here, we examine evidence for pulsed evolution across ver- rates of evolution. One way to reconcile these observations is to tebrate taxa, using a method for fitting Lévy processes to com- imagine that evolution proceeds in pulses, rather than in incre- parative data. These processes can capture both incremental and ments, on geological timescales. To test this hypothesis, we devel- pulsed modes of evolution in a single, simple framework. We oped a maximum-likelihood framework for fitting Levy´ processes apply this method to analyze 66 vertebrate clades containing to comparative morphological data. This class of stochastic pro- 8,323 extant species for evidence of pulsed evolution by compar- cesses includes both an incremental and a pulsed component. We ing the statistical fit of several varieties of Lévy jump processes found that a plurality of modern vertebrate clades examined are (modeling different types of pulsed evolution) to three models best fitted by pulsed processes over models of incremental change, that emphasize alternative macroevolutionary dynamics. Under stationarity, and adaptive radiation. When we compare our results these models, the adaptive optimum of a lineage may wan- to theoretical expectations of the rate and speed of regime shifts der incrementally and freely (Brownian motion), it may change for models that detail fitness landscape dynamics, we find that our incrementally but remain stationary (Ornstein–Uhlenbeck), or it quantitative results are broadly compatible with both microevolu- may change most rapidly following the initial diversification of a tionary models and observations from the fossil record. clade while decelerating over time, e.g., during an adaptive radiation (early burst). Beyond simple model comparison, we show macroevolution | Levy process | pulsed evolution | adaptive landscape that the parameter estimates corresponding to the microevolutionary and macroevolutionary mechanisms of the model have key debate in evolutionary biology centers around the seem- biologically meaningful interpretations (2), illuminating previ- Aing contradictions regarding the tempo and mode of evo- ously hidden features of Simpson’s adaptive grid. lution as seen in fossil data compared with ecological data. Results Fossil data often support models of stasis, in which little evolutionary change is seen within lineages over long timescales (1, Maximum-Likelihood Method Has Power to Distinguish Pulsed 2), while ecological data show that rapid bursts of evolution are Evolution from Comparative Data. We developed a maximum- not only possible, but potentially common (3, 4). At face value, likelihood method for fitting Lévy processes to phylogenetic these observations seem to contradict one another, an observa- comparative data using restricted maximum-likelihood estimation known as the “paradox of stasis” (5). These observations are tion (REML), by analyzing the phylogenetically independent often reconciled through a descriptive model of pulsed evolution, contrasts (16) (Materials and Methods). The Lévy processes we entailing stasis interrupted by pulses of rapid change, as famously apply in this work consist of two components: a Brownian motion articulated by Simpson (6). and a pure jump process. The Brownian motion is characterized On macroevolutionary timescales, pulses of rapid change are expected to look roughly instantaneous. Only recently have sta- Significance tistical methods grown sophisticated enough to model pulsed evolution as a stochastic process, with advances showing that The diversity of forms found among animals on Earth is strik- punctuation is detectable in some fossil time series (7) and ing. Despite decades of study, it has been difficult to reconcile between pairs of living and extinct taxa (8). the patterns of diversity seen between closely related species While these studies establish the existence of pulsed evolution, with those observed when studying single species on eco- it is still unknown whether the evolutionary mode is common or logical timescales. We propose a set of models, called Levy´ rare. How many clades in the Tree of Life were shaped by abrupt processes, to attempt to reconcile rapid evolution between pulses of rapid evolution? If these evolutionary pulses are com- species with the relatively stable distributions of phenotypes mon, then that should inform our expectations about how traits seen within species. These models, which have been success- evolved for clades that left no fossils and the potential for vulner- fully used to model stock market data, allow for long peri- able species to adapt rapidly to climate change (9). To this end, ods of stasis followed by bursts of rapid change. We find that phylogenetic models—models of trait evolution that account for many vertebrate groups are well fitted by Levy´ models com- the shared ancestry of species—have played a vital role in mea- pared with models for which traits evolve toward a stationary suring the relative support of competing Simpsonian modes of optimum or evolve in an incremental and wandering manner. evolution. A pioneering meta-analysis (10) fitted a collection of phyloge- Author contributions: M.J.L. and J.G.S. designed research, performed research, analyzed netic models to 49 animal clades, finding preference for modes of data, and wrote the paper. incremental, but not explosive, evolutionary change. That work The authors declare no conflict of interest. predated the advent of phylogenetic models of pulsed evolution This article is a PNAS Direct Submission. (11, 12), so its frequency could not have been measured. More- This open access article is distributed under Creative Commons Attribution- over, there remains a concern that models of incremental and NonCommercial-NoDerivatives License 4.0 (CC BY-NC-ND). pulsed change leave similar patterns of trait variation in neonto- See Commentary on page 13068. logical data (13, 14). While recent methodological developments 1To whom correspondence should be addressed. Email: [email protected]. show that there is power in comparative data to identify pulsed This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10. evolution (11, 12, 15), little is known about the statistical proper- 1073/pnas.1710920114/-/DCSupplemental.

13224–13229 | PNAS | December 12, 2017 | vol. 114 | no. 50 www.pnas.org/cgi/doi/10.1073/pnas.1710920114 Downloaded by guest on September 24, 2021 Downloaded by guest on September 24, 2021 oiiertsfrietfigple vlto,ee ntepres- with the clades false in for low (4% even error saw evolution, phylogenetic of we pulsed ence Moreover, identifying distribu- Appendix). for heavy-tailed the rates (SI a to positive change in due trait resulting is of jumps This tion large evolution. rare, evolution of of (>100 pulsed modes impact differentiate clades Simpsonian to sized other power from moderately sufficient had with between data we simulations comparative distinguish taxa), For from to 14). models impossible incremental (13, is certain it and that pulsed speculation to ( time ing to proportionally variance accumulate (18). anagenesis” any “punctuated at as occur theory known may classical sometimes pulses the time, Instead, in (17). as equilibrium cladogenesis, punctuated to of evolution of interval pulses the ple in time size short a the with in jump occurring a of probability the as L a by ized parameter, rate a by adsadSchraiber and Landis evo- particular a that evidence any find not About trait of did mode respectively). single We any 2%, for sub- evolution. support and selected decisive lacked 14%, each clades of were (18%, 34% OU often and less EB, stantially BM, evolution. pulsed of in distribution. found normal be can a L tion different using each how noise intraspe- of sampling pro- Examples modeled and jump further and variation We Brownian cific BM+NIG. the and of BM+JN Finally, possible. combination cesses, still the zone, are adaptive examined zones an adaptive we of between width shifts the rare within but occurs the where change change, of phenotypic model majority jump- constant this of constantly times; dynamics waiting is the longer process captures to requiring NIG jumps this the larger use with hand, adaptive ing, we other between value; the shifts new On large-scale zones. a by to followed jumping stasis represent before time distributed exponentially of dis- an for amount waits normally process Gaus- JN inverse with The normal types (NIG). the Poisson sian and different (JN)] compound normal two [jump the jumps compared tributed processes: also We evo- jump of time. of tempo over the which slows in lution radiation, (EB) burst adaptive early capture the to and model the optimum evolu- stationary used single incremental a We model around tion to optimum. lin- model motion wandering a (OU) Brownian which a Ornstein–Uhlenbeck a in follows change, used phenotype phenotypic We eage’s incremental models. each model of for to panel (BM) 20) a (19, from (wAICc) verte- dataset weights size-corrected major sample criteria the five information computed across Akaike We clades 1). 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EVOLUTION SEE COMMENTARY Thamnophilidae dict similar rates of shifting between adaptive zones, indicated by Rhinolophoidea+allies Columbidae the fact that the solid curves are near each other for z ≥ 2. When Sphaerodactylidae looking at a clade that is best fitted by a jump-diffusion model, Ranoidea Gekkonidae II such as Anguimorpha (Fig. 3B, Right), we find that they explain Boidae+allies most of the morphological disparity among taxa via the BM com- Elapidae Picidae ponent of the model, and we see that jumps occur extremely Holocentridae rarely compared with pure jump models. Jump-diffusion models Ramphastidae Xenodontinae with small diffusion components produce jump size–time curves Clupeiformes that are essentially identical to the jump size–time curves for the Atheriniformes Liolaemidae corresponding pure jump model (compare NIG and BM+NIG Natricinae for Muroidea). Percomorphaceae Accipitridae Psittacidae I Discussion Balistidae Noctiolionoidea The pulses of rapid evolution proposed by Simpson (6) are evi- Phrynosomatidae dent in ecological (3, 4) and paleontological (23) observations. Labridae Because of their rapidity relative to geological timescales, such Dactyloidae Diplodactylidae phenotypic “jumps” are difficult to observe directly (24, 25), Lygosominae II but their lasting impressions are detectable in both simulated Vespertilionidae Chaetodontidae and empirical comparative phenotypic datasets (Fig. 1). Among Scolopaci Simpsonian modes of phenotypic macroevolution—including Hyloidea I Procellariidae unconstrained incremental evolution, evolutionary stationarity, Anatinae explosive evolution, and pulsed evolution—we found that pulsed Cucuildae Pomacentridae evolution is not only detectable, but also a preferred explana-

Clade Tropiduridae tion for how body sizes evolved among diverse vertebrate groups. Cetacea Lamprophiidae Phenotypic variation accrues in time at a rate that is nearly iden- Etheostoma tical when assuming models of nonstationary incremental evolu- Hyloidea II Agamidae tion vs. pulsed evolution; that is, they differ in evolutionary mode Loricariinae rather than evolutionary tempo. Lari Lygosominae I To test for the signatures of different modes of evolution, Colubrinae we assembled neontological comparative datasets for 66 verte- Strigidae Acanthuridae brate clades, composed of time-calibrated phylogenies and body Bovidae size measurements (Table 1). Importantly, we undertook the call Gekkonidae I Caudata for “broad comprehensive sampling” that is necessary to char- Lacertidae acterize tempo and mode of evolution without bias (26). We Psittacidae II Marsupialia developed a method to fit a model of phylogenetic evolution Carnivora of continuous traits for processes that model macroevolution- Gymnophthalmoidea Anguimorpha ary jumps by exploiting the mathematical properties of Lévy pro- Chamaeleonidae cesses. Applying our method to the vertebrate dataset, we found Muroidea Tityridae+Tyrannidae that body size evolution was best explained by jump models in Viperidae 32% of vertebrate clades when fitting incremental, stationary, Testudines Gerrhosauridae+Cordylidae and explosive models of evolution along with four flavors of Trochilidae jump processes. Taking a broader definition of support for mod- Primates Furnariidae els that concentrate, rather than evenly distribute, evolutionary Phasianidae change, pulsed and EB models are selected for 45% of all clades Cyprinidae and for 70% among those clades with strong model preference Model support (wAICc) of any kind. This suggests future work to explore the interac- tion of EB and pulsed models, in which the rate and/or magni- Incremental change Explosive change tude of evolutionary pulses decay following the initial radiation Incremental stationarity Pulsed change of a clade. Simulated datasets with phylogenetic error do not result in a Fig. 1. Model selection profiles for 66 vertebrate clades. Clade colors indicate their order: black, fish; purple, amphibians; green, reptiles; blue, systematic bias toward preferring Lévy processes over competing birds; and red, mammals. Each clade was fitted to seven models, classified models (SI Appendix, Fig. S2). We found that, if anything, our into four groups: incremental change (BM), incremental stationarity (OU), data-filtering and model selection procedures tip the balance to explosive change (EB), and pulsed change (JN, NIG, BM+JN, BM+NIG). AICc incorrectly favor nonpulsed over pulsed models of evolution. The weights were computed using only the best-fitting model within each class. false positive rates seen in simulations are four to seven times A model class is selected only if its AICc weight is twice as large than that lower than the rates of clades that are best fitted by Lévy pro- of any other model class (circles indicate selection counts: 12 incremental cesses in the empirical data, suggesting a very low false discov- change, 1 incremental stationarity, 9 explosive change, 21 pulsed change, 23 ery rate. These findings contradicted concerns that incremental ambiguous). Alternative model classifications are provided in SI Appendix. and pulsed models would be difficult to distinguish, because BM models and jump processes result in the same tempo of evolu- changes within a lineage’s adaptive zone occur on approximately tion (measured by the variance that the processes accumulate the same timescale as jumps between adaptive zones. In contrast, per unit time). Nonetheless, rare, large jumps result in heavy- infinitely active processes, as represented by NIG, jump continu- tailed distributions of trait change along branches (quantified by ously. Under these models, shifts within an adaptive zone occur the excess kurtosis of the trait change distribution), which can be frequently, which could reflect rapid adaptation to small-scale distinguished from incremental evolution occurring at a similar environmental perturbations, while larger shifts between adap- tempo. In the empirical dataset, we found no support that cer- tive zones occur on much longer timescales. Interestingly, we tain model classes were overrepresented within a particular ver- find that both finite and infinite activity pure jump models pre- tebrate group (SI Appendix, Table S2). One possibility is that the

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EVOLUTION SEE COMMENTARY dynamics, such as logistic diversification (34), may provide a suf- groups. Clades were generally either extracted from large, taxon-rich phylo- ficiently strong signal to disentangle anagenetic and cladogenetic genies (amphibians, reptiles, birds) or pooled across independently estimated models of pulsed evolution. phylogenies (fish, mammals). Availability and quality of trait data varied We found that different kinds of jump processes, represent- between vertebrate groups, each requiring special handling. ing different modes of rapid evolution (constant rapid adap- Fish. Standard, fork, and total lengths were extracted from Fishbase, using RFishbase (43). For each fish clade, we used an allometric regression to con- tation vs. long periods of stasis broken up by jumps between vert all taxa to the most frequently observed length type (44). adaptive zones), leave faint, but unique, signatures in phyloge- Amphibians. Mean female snout-vent lengths were used for the three Anu- netic data. By integrating these models into fossil sequences, we ran clades (Ranoidea, Hyloidea I, and Hyloidea II). Caudata traits were drawn suspect that further fine-scale details of macroevolution can be from ref. 39. elucidated. Moreover, in quantitative finance, where the “fos- Reptiles. Total lengths were used for all snake (Serpentes) clades. Maximum sil record” of stock prices through time is perfectly kept, fine- straight-line carapace lengths were used for turtles (Chelonia). Snout-vent scale dynamics of jump processes can be inferred (35, 36), sug- lengths were used for all remaining reptile clades. gesting that such power exists for suitably densely sampled fossil Mammals. Adult unsexed body mass measurements were used. sequences. Our approach, which uses only modern data but inte- Birds. Adult sex-averaged mean body mass measurements were used. Data treatment. We corrected for two sources of measurement error that grates them into a phylogenetic framework, represents an impor- would potentially mislead model selection tests to favor Levy´ processes. First, tant step toward a fully integrative analysis of macroevolutionary rounding error in the trait data caused some clades to contain contrasts that processes. have the exact value of zero. Zero-valued contrasts artificially favor the JN process, which contains a singularity at 0. Second, grossly inaccurate mea- Materials and Methods surements and/or phylogenetic error will drive some portion of contrasts to Likelihoods Using Characteristic Functions. Because most Levy´ processes are appear excessively large, fattening the tail density of the trait distribution. To known only by their characteristic function, we developed a REML algorithm mitigate such errors, we first pruned away any subclades with zero-valued that operates on characteristic functions. We computed the likelihood of the contrasts for all clades. Then, assuming a BM model, we pruned away the independent contrasts by proceeding from the tips to the root of the phy- subclade with the most extreme valued contrast for 63 of 66 clades. The logeny. To do so, we recursively update the estimate of the trait at internal three clades exempted from the second filtering step either had a large, but nodes as a linear combination of the trait value at the two daughter nodes. expected, contrast (Anguimorpha, involving the contrast containing Varanus We also include an additional term to model the uncertainty in trait values komodoensis) or had the largest contrast fall near the base of the tree (Procel- at the tips of the tree due to both intraspecific variation and measurement lariidae and Thamnophilidae). The filtering procedures resulted in a 4.7% loss error. Details of the algorithm can be found in SI Appendix. of data (8,323 of 8,729 taxa remained). SI Appendix contains further details regarding how the input data were processed. Optimizing Model Fit Using REML. To fit the model to data, we used the R programming language and relied on several R packages (37–39). Our pack- Empirical Model Selection. We computed sample size-corrected AIC weights age is available at https://github.com/Schraiber/pulsR. Optimal parameter (wAICc) for each clade across four model classes: BM, OU, EB, and Levy´ pro- values are obtained by maximizing the likelihood, using the Nelder–Mead cesses (Fig. 1). The Levy´ process with the highest AICc score was chosen to simplex method (40). To ensure that we obtained true maximum-likelihood represent all Levy´ processes within the class. Model selection required the estimates, we performed multiple independent parameter searches (10 for model class to be at least twice as probable as any competing model class. empirical data, 4 for simulated data). In addition, we validated that all With BM being a special case of the remaining six models, this threshold lies maximum-likelihood estimates agreed with model hierarchies; e.g., the on the cusp of the maximum relative probability that it might receive under maximum likelihood for OU must be greater than or equal to that for BM. wAICc. Numerous alternative analyses under various model classifications and assumptions are located in SI Appendix. Simulation Study for Model Selection Power and Sensitivity. We assessed the power and false positive rate of our method by manipulating tree size and Expected Waiting Time Between Adaptive Shifts. For Levy´ processes with a phylogenetic error in a controlled simulation setting. Each dataset was sim- jump component, we are interested in the waiting time until a jump outside ulated by sampling one tree from an empirical posterior distribution of of the current adaptive zone occurs. Under the symmetric jump models we trees (41) and then simulating trait data under each of the seven candi- consider here, the waiting time for a jump larger than x is date models (BM, OU, EB, JN, NIG, BM+JN, BM+NIG). Simulation parameters are given in SI Appendix, Table S1. We then computed AIC weights for ¯ 1 each of the seven datasets across the same seven candidate models, once t(x) = ∞ . 2 R ν(ds) under the originally sampled tree (the “true” tree) and then again under x the maximum clade credibility tree that summarizes the posterior (the “con- We characterized the width of adaptive zones by the amount of intraspecific sensus” tree). Repeating this procedure 100 times, we counted how often variation in a clade. To provide an accurate estimate of intraspecific varia- each model type is selected in the presence and absence of tree error. This tion for all clades, we regressed our observed values of σ against direct experiment was conducted for two clades with sizes representative of our tip measurements of intraspecific SD in birds (59) (n = 16, P < 0.005, R2 = 0.53, empirical datasets (Procellariidae with 106 taxa and Tityridae, Tyrannidae, slope = 0.200, intercept = 0.059). Further details for this analysis and results and allies with 325 taxa). In total, we simulated 1,400 datasets and per- using the uncorrected σ estimates are given in SI Appendix. formed 39,200 maximum-likelihood fittings. tip ACKNOWLEDGMENTS. We thank Damien Wilburn, Tracy Heath, and Ignacio Vertebrate Dataset. We compiled numerous phylogenetic and trait measure- Quintero for helpful comments on an early version of this manuscript. ment resources to measure body size evolution (Table 1). The species relation- Jonathan Chang, Peter Cowman, and Nathan Upham provided invalu- ships within each clade were represented using fixed phylogenies with branch able advice on constructing the empirical datasets. Discussions with Joe lengths measured in millions of years. Body size data were represented by Felsenstein helped direct the early course of this project. The comments body length for fish, amphibians, and reptiles and, mass being a function of of two anonymous reviewers greatly improved the clarity and readabil- volume, by the cube root of body mass for mammals and birds. Trait mea- ity of the manuscript. J.G.S. was supported in the early stages of this work by National Science Foundation (NSF) Postdoctoral Fellowship DBI- surements were then log transformed, under the assumption that trait evo- 1402120 and subsequently by startup funds from Temple University. M.J.L. lution operates on a multiplicative scale (42). Handling the data in this manner was supported initially by the Donnelley Fellowship through the Yale Insti- permits the comparison of evolutionary parameters between clades because tute of Biospheric Studies and later through NSF Postdoctoral Fellow- our body size and tree data share a common scale. Broadly, we applied the ship DBI-1612153. Analyses were performed on the Yale High-Performance same data assembly strategy to all clades within each of the five vertebrate Computing clusters.

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